We did not take personalities into account here, we looked only at the swing states and what they are likely to vote from a purely statistical view. Giving odds can be dangerous indeed, but such as they are given several assumptions, the odds in Obama’s favor seem to be at least 20:1, or even twice that—just from the numbers.
Explicit assumptions:
- Poll Tracker Swing States Provides accurate data that is representative.:
- Voters likely to vote actually do so in an average turnout of voters.
- Samples of likely voters are large enough to provide small margins of error.
- The swing states selected by the polls are indeed those most likely to swing. This is merely probable, not certain.
- We are assuming Romney holds all states that typically vote red while Obama will win all states normally voting blue.
- No serious political issues beyond those present arise between now and election day.
- World and economic events will continue to develop as they have in recent months.
- Neither candidate changes their message or campaign style in a major way. If either does, it could go either way.
Criteria for counting delegates, state-by-state.
- Likely winner of a state leads by at least two standard deviations, two sigma; <5% chance of error. Sigma was derived from the variance (defined below).
- Leaning toward winner by at least one standard deviation, one sigma; derived from the preference variance of the 12 swing states: Ohio, Va, Fla, N.C., Colo, Pa, Iowa, Nev, Wis, N.M., Mich, N.H.
- Too close to call includes all others swing states.
With this design, let’s see what the 21 Sept 12 poll referenced adds up to statistically.
- Obama winner: 117 delegates.
- Obama leaning: 15 delegates
- Too Close to call: 19 delegates
Points that can be made as of 21 Sept 2012:
- Romney has an uphill battle (estimated as > 20:1 against him) that looks not to be winnable in spite of his vast financial advantage.
- Obama can ill afford a political or economic debacle.
- Without a major, major gaff on the part of one or the other candidate, the coming debates are not likely to change the projected outcome by much.
Politics and world events are notoriously variable; nothing is ever certain, but statistical projections are better than guesses. 46 days left: Vote your choice on 6 Nov 2012.
We close with a technical point: Variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value). In particular, the variance is one of the moments of a distribution. In that context, it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity. See Wikipedia.
Posted by RoadToPeace on Friday, September 21, 2012.
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